# Geometry Trigonometry

## Presentation on theme: "Geometry Trigonometry"— Presentation transcript:

Geometry Trigonometry
Do Bees Build It Best? Geometry Trigonometry

BUILDING THE BEST

NAILING DOWN AREA

HOW MANY CAN YOU FIND?

THAT’S ALL THERE IS!

PARALLELOGRAMS AND TRAPEZOIDS

FORMING FORMULAS

GOING INTO THE GALLERY

A RIGHT-TRIANGLE PAINTING

A TRIGONOMETRIC SUMMARY

MORE GALLERY MEASUREMENTS

TRI-SQUARE RUG GAMES

ANY TWO SIDES WORK LEG^2 + LEG^2 = HYP^2

IMPOSSIBLE RUGS

MAKE THE LINES COUNT

PROOF BY RUGS

THE POWER OF PYTHAGORAS

LESLIE’S FERTILE FLOWERS

FLOWERS FROM DIFFERENT SIDES

DON’T FENCE ME IN

RECTANGLES ARE BORING!

MORE FENCING, BIGGER CORRALS

BUILDING THE BEST FENCE

FALLING BRIDGES

LESLIE’S FLORAL ANGLES

FLAT CUBES

FLAT BOXES

THE INS AND OUTS OF BOXES

A SCULPTURE GARDEN

THE WORLD OF PRISMS

SHEDDING LIGHT ON PRISMS

PYTHAGORAS AND THE BOX

BACK ON THE FARM

WHICH HOLDS MORE?

CEREAL BOX SIZES

A-TESSELLATING WE GO

A PORTFOLIO OF FORMULAS

THAT’S ALL THERE IS! EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS
EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

FORMING FORMULAS LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

GOING INTO THE GALLERY REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

A RIGHT-TRIANGLE PAINTING
DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

A TRIGONOMETRIC SUMMARY
SIN A = OPPOSITE/HYPOTENUSE COS A = ADJACENT/HYPOTENUSE TAN A = OPPOSITE/ADJACENT

A HOMEMADE TRIG TABLE DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP MEASURE ALL THE SIDES COMPUTE THE RATIOS OF SIN, COS, AND TAN

MORE GALLERY MESUREMENTS
SIN A = OPPOSITE/HYPOTENUSE COS A = ADJACENT/HYPOTENUSE TAN A = OPPOSITE/ADJACENT

TRI-SQUARE RUG GAMES AL WINS WHEN THE LARGEST OF THE 3 SQUARES HAS THE MOST AREA. WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

TRI-SQUARE RUG GAMES BETTY WINS IF THE TWO SMALLER SQUARES HAVE MORE AREA THEN THE LARGEST WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

TRI-SQUARE RUG GAMES IF THE TWO SMALLER SQUARES HAVE THE SAME AREA AS THE LARGEST, THIS IS A FAIR GAME. WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

ANY TWO SIDES WORK

ANY TWO SIDES WORK

ANY TWO SIDES WORK

IMPOSSIBLE RUGS RULE: ANY TWO SIDES OF A TRIANGLE MUST BE GREATER THAN THE THIRD SIDE

MAKE THE LINES COUNT

THE POWER OF PYTHAGORAS

THE POWER OF PYTHAGORAS

LESLIE’S FERTILE FLOWERS

FLOWERS FROM DIFFERENT SIDES

DON’T FENCE ME IN RANCHER GONZALES CAN ONLY AFFORD 300 FEET OF FECNING
MAKE AN INOUT TABLE OF VARIOUS LENGTHS AND WIDTHS

RECTANGLES ARE BORING! RANCHER GONZALE’S NEPHEW JUAN HAS SUGGESTED RECTANGLES AGAIN SHE MUST USE 300 FEET OF FENCING

MORE FENCING, BIGGER CORRALS
HOW DOES THE AREA OF A SQUARE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

MORE FENCING, BIGGER CORRALS
HOW DOES THE AREA OF A AN EQUILATERAL TRIANGLE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

ACES : PENTAGON TWO’S: HEXAGON THREE’S: SEPTAGON FOUR’S: OCTAGON FIVE’S: 9 SIDED REG-POLY SIXE’S: 10 SIDED REG-POLY

BUILDING THE BEST FENCE
AREA= (P^2/4n) * tan (90-180/n)

FALLING BRIDGES USE OTHER APPROXIMATIONS FOR THE SQUARE ROOT OF 2

LESLIE’S FLORAL ANGLES
REMEMBER, THE INVERSE OF: ADDING? MULTIPLYING? SOMETHING SQUARED? NOW WE NEED THE INVERSE OF OUR TRIG FUNCTIONS

FLAT BOXES 132 CM SQUARED

FLAT BOXES 108 CM SQUARED

A VOLUMINOUS TASK SURFACE AREA VOLUME #1 #2 #3 #4 #5

A VOLUMINOUS TASK SURFACE AREA VOLUME #7 #8 #9 #10

THE INS AND OUTS OF BOXES

A SCULPTURE GARDEN FIND A WAY TO ARRANGE 8 CUBES THAT USES THE LEAST AMOUNT OF PAINT

THE WORLD OF PRISMS PRISM IS A SPECIAL TYPE OF SOLID GEOMETRIC FIGURE
THE INTIAL AND FINAL FACES ARE THE BASES USUALLY 1 OR 2 BASES PERPENDICULAR DISTANCE BETWEEN THE BASES IS THE HEIGHT

THE WORLD OF PRISMS TRIANGULAR PRISMS HEXAGONAL PRISMS
RECTANGULAR PRISMS

THE WORLD OF PRISMS RIGHT PRISMS OBLIQUE PRISMS

THE WORLD OF PRISMS LATERAL FACES LATERAL EDGES BASES
LATERAL SURFACE AREA TOTAL SURFACE AREA

PYTHAGORAS AND THE BOX

BACK ON THE FARM